Application of radial basis functions neutral networks in spectral functions

The reconstruction of the spectral function from the correlation function in Euclidean space is a challenging task. In this paper, we employ the machine learning techniques in terms of the radial basis functions networks to reconstruct the spectral function from a finite number of correlation data. To test our method, we first generate one type of correlation data using a mock spectral function by mixing several Breit-Wigner propagators. We found that compared with other traditional methods, e.g., truncated singular value decomposition, Tikhonov, and maximum entropy methods, our approach gives a continuous and unified reconstruction for both positive definite and negative spectral functions, which is especially useful for studying the QCD phase transition. Moreover, our approach has considerably better performance in the low-frequency region. This has advantages for the extraction of transport coefficients which are related to the zero frequency limit of the spectral function. With the mock data generated through a model spectral function of stress energy tensor, we find our method gives a precise and stable extraction of the transport coefficients.